Cooperation-conflict dynamics and ecological resilience under environmental disturbances

Ecosystem stability is increasingly threatened by rapid environmental fluctuations that alter species interactions and survival strategies. Traditional steady-state analyses often overlook transient dynamics that govern ecosystem responses to accelerating change. This study explored rate-induced tipping (R-tipping), a phenomenon where environmental change rates outpace species' adaptive capacity, triggering abrupt shifts between ecological states. Our findings demonstrate that species persistence depends on a delicate balance between cooperation-associated costs, population densities, and environmental variation rates. Under moderate fluctuations, species can track unstable states before reaching new equilibria, enhancing resilience. However, beyond critical thresholds, homoclinic and saddle-node bifurcations destabilize coexistence induced with increasing cooperation strength, leading to extinction cascades. By integrating time-dependent basin stability analysis, we uncovered mechanisms driving ecological transitions and identified key factors influencing long-term persistence. This research highlights the need for dynamic models to predict tipping events and informs conservation strategies for mitigating biodiversity loss in rapidly changing environments.